1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lorico [155]
3 years ago
5

The area of a rectangle is 99 ft^2, and the length of the rectangle is 7 more than double the width. Find the dimensions of the

rectangle.
Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

width =5.5ft

length =18

Step-by-step explanation:

w=x

L=2x+7

area=w*L

99 = x(2x+7)

99=2x^{2} +7x

2x^{2} +7x-99=0

2x^{2} +18x-11x-99=0

2x(x+9)-11(x+9)=0

(2x-11)(x+9)=0

2x-11=0

2x=11

x=11/2

x=5.5

L=2x+7=2*5.5+7=11+7=18

You might be interested in
Can someone thoroughly explain this implicit differentiation with a trig function. No matter how many times I try to solve this,
Anton [14]

Answer:

\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}

Step-by-step explanation:

So we have the equation:

\tan(x-y)=\frac{y}{8+x^2}

And we want to find dy/dx.

So, let's take the derivative of both sides:

\frac{d}{dx}[\tan(x-y)]=\frac{d}{dx}[\frac{y}{8+x^2}]

Let's do each side individually.

Left Side:

We have:

\frac{d}{dx}[\tan(x-y)]

We can use the chain rule, where:

(u(v(x))'=u'(v(x))\cdot v'(x)

Let u(x) be tan(x). Then v(x) is (x-y). Remember that d/dx(tan(x)) is sec²(x). So:

=\sec^2(x-y)\cdot (\frac{d}{dx}[x-y])

Differentiate x like normally. Implicitly differentiate for y. This yields:

=\sec^2(x-y)(1-y')

Distribute:

=\sec^2(x-y)-y'\sec^2(x-y)

And that is our left side.

Right Side:

We have:

\frac{d}{dx}[\frac{y}{8+x^2}]

We can use the quotient rule, where:

\frac{d}{dx}[f/g]=\frac{f'g-fg'}{g^2}

f is y. g is (8+x²). So:

=\frac{\frac{d}{dx}[y](8+x^2)-(y)\frac{d}{dx}(8+x^2)}{(8+x^2)^2}

Differentiate:

=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}

And that is our right side.

So, our entire equation is:

\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}

To find dy/dx, we have to solve for y'. Let's multiply both sides by the denominator on the right. So:

((8+x^2)^2)\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}((8+x^2)^2)

The right side cancels. Let's distribute the left:

\sec^2(x-y)(8+x^2)^2-y'\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy

Now, let's move all the y'-terms to one side. Add our second term from our left equation to the right. So:

\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy+y'\sec^2(x-y)(8+x^2)^2

Move -2xy to the left. So:

\sec^2(x-y)(8+x^2)^2+2xy=y'(8+x^2)+y'\sec^2(x-y)(8+x^2)^2

Factor out a y' from the right:

\sec^2(x-y)(8+x^2)^2+2xy=y'((8+x^2)+\sec^2(x-y)(8+x^2)^2)

Divide. Therefore, dy/dx is:

\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)+\sec^2(x-y)(8+x^2)^2}

We can factor out a (8+x²) from the denominator. So:

\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}

And we're done!

8 0
3 years ago
-3x+4=-17<br>show how you did it
Oxana [17]
-3x+4=-17
subtract -4 from both sides
divide -3 from both sides
the answer is 7
8 0
3 years ago
Extreme cold and hot temperatures are known to affect the operation of electronic components. Winter is approaching and you are
Musya8 [376]

Answer:

A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

Test statistic(Z) = 2.31

P-value = 0.0104

Step-by-step explanation:

Step 1

Null hypothesis: The average damaging temperature of nine iPods is 5°F

Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F

Step 2

Mean=5°F, Sd=3, df=n-1=9-1=8

The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306

Confidence Interval(CI) = (mean + or - t×sd/√n)

CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F

CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F

Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31

Step 3

Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896

P-value = 1 - 0.9896 = 0.0104

Step 4

Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

7 0
3 years ago
Eli has 7 games on his phone. His sister has 6 more than him. Which ratio compares the number of games on Eli’s phone to the num
sergij07 [2.7K]

Answer:

1 to 1.89 or 1:1.89

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Margo is practicing her free throws for basketball
kipiarov [429]

Answer:

16

Step-by-step explanation:

Well if you think about it, if she has a total of 10 attempts she has to make 8 of them to make it on the team. Now the total attempts is double so we double the number of throws she needs to make in order to make the team so to do this we would do 8*2 which is 16. She needs to make 16 throws to make it on the team.

5 0
3 years ago
Other questions:
  • Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of $29. For any minutes over 250, Tracy is
    11·2 answers
  • A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the
    9·2 answers
  • Gena attached a dog ramp to her sofa, which allows her oldest dog to easily climb onto a seat cushion. The ramp is 55 inches lon
    5·1 answer
  • 3 ( 4x + 8 )+ 3 ( 2x - 6 )​
    9·2 answers
  • Solve the equation I= prt for t <br><br> A- t= ipr<br> B- t=I/pr<br> C- t= pr/I
    7·1 answer
  • When solving an inequality, you must ____________ the variable.
    14·1 answer
  • Can you figure this out? Math kills me!
    12·2 answers
  • Help me find the value of k asap please!<br><br>5/4(2 - k) = 2(3k - 1) - 2/3k
    10·1 answer
  • Jeffrey can jog 5 miles in 40 minutes. How many more miles can he jog in 90 minutes than in 40 minutes? Assume the relationship
    9·1 answer
  • Given: 2x + b &gt; -3. Find the value of b so that x &gt; 3<br>Help a s a p please
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!